If you are interested in learning, the idea of memristors (and other computational memory technology) is not to replace traditional memory, but rather to augment small portions of it with increased/additional computational functionality.
For example, you could add a (relatively speaking) extremely small number of memristors to an existing memory module, load two matrices into that area of memory, and reading from the adjacent region of memory would immediately yield the result of multiplying those two matrices. If you could simply instruct the RAM module where the existing data lies, this would be an immense boost in efficiency to AI/deep learning prediction algorithms. Here is a video explanation of how this could be use to perform matrix vector multiplication in O(1): https://youtu.be/30K5i8bdiyg?t=1492 .
That video mentions later that something similar can be used in solving linear and partial differential equations. Applications for deep learning training is discussed at 40:20 .
You'll notice everything discussed in the keynote has experimental results. At 41:27, he mentions that you can actually send images to their memristor chip over their website . Though the link is unfortunately dead, it definitely worked, and was in fact performing neural network computations using memristors over the network.